The goal of representation learning is to embed real-world data, frequently modeled on a graph, into an ambient space. The structure of this embedding space can then be used to analyze and perform tasks on the discrete graph.
The predominant approach has been to embed discrete structures in an Euclidean space. Nonetheless, data in many domains including social [1]}, [2]}, sensor [3]}, gene [4]}, protein molecular [5]} and complex [6]} networks or the Internet [7]} exhibit non-Euclidean features, making embeddings into Riemannian manifolds with a richer structure necessary.
For this reason, embeddings into hyperbolic [8]}, [9]}, [10]}, [11]}, [12]} and spherical spaces [13]}, [14]} have been developed.
Recent work proposes to combine different curvatures through several layers [15]}, [16]}, or to enrich the geometry by considering Cartesian products of spaces [17]}, [18]}, [19]}.
However, their ability to model complex patterns is inherently bounded by the geometric properties of the target embedding space, which has to be picked beforehand.
The choice of a metric space where to embed the data can be understood as selecting an inductive bias [19]}, which does not always adapt to all parts of the graphs.
